practical file of numerical methods in engineering

Upload: gurjinder-romana

Post on 04-Apr-2018

221 views

Category:

Documents


0 download

TRANSCRIPT

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    1/43

    @l

    F~on{ehib Onsj`cx ef Nfaefnn{efa

    ]S^ Aeife Wieb Xefaj Hio}~x

    Kisjefci

    Fion/A~{gefcn{ Xefaj

    [`bb F`&9==8999;5:1=

    Onhjifehib

    > sj Xnonxsn{

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    2/43

    X&F`& S@]EH ]ianF`&

    Xeafis~{n

    9& S` lefc sjn {``s `l Ibank{ieh Ny~ise`f~xefa Kexnhse`f Onsj`c& 9/8

    ;& S` lefc sjn {``s `l S{ifxhnfcnfsib Ny f ~xefa Kexnhse`f Onsj`c& 3/>

    8& S` lefc sjn {``s `l Ibank{ieh Ny~ise`f~xefa [na~bi/Libxe Onsj`c& & S` lefc sjn {``s `l Ibank{ieh Ny~ise`f~xefa Fnqs`f/[i}jx`f Onsj`c& 99/9;

    /91

    :&S` lefc sjn x`b~se`f `l Xeo~bsifn`~xNy~ise`fx ~xefa Ai~xx G`{c`f Onsj`c&

    9:/;9

    5&S` lefc sjn |ib~n `l l*z% l{`o sjn ae|nfcisi ~xefa Bia{ifanx Efsn{}`bise`fOnsj`c&

    ;;/;3

    9=&S` lefc sjn x`b~se`f `l @{cefi{uCelln{nfseib Ny f ~xefa N~bi{ Onsj`c&

    ;>/;1

    99&S` lefc sjn x`b~se`f `l @{cefi{uCelln{nfseib Ny f ~xefa [~fan/ D~ssiOnsj`c `l ; fc @{cn{&

    ;:/;5

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    3/43

    X&F`& S@]EH ]ianF`&

    Xeafis~{n

    9;&S` lefc sjn x`b~se`f `l @{cefi{uCelln{nfseib Ny f ~xefa [~fan/ D~ssiOnsj`c `l 3 sj `{cn{

    8=/89

    98&S` les sjn xs{ieajs befn *u?iz$ k% `f ae|nfcisi ~xefa onsj`c `l bnixs xy~i{nx&

    8;/83

    93&Les sjn H~{|n * u?iz ; $kz $h % `f ae|nfcisi ~xefa onsj`c `l bnixs xy~i{nx

    8>/8:

    9>&S` les sjn Nz}`fnfseib H~{|n*u?in kz%`fae|nf cisi ~xefa onsj`c `l bnixs xy~i{nx&

    85/3=

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    4/43

    9

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn {``s l Ibank{ieh Ny~ise`f~xefa Kexnhse`f Onsj`c&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j6(efhb~cn2h`fe`&j6lb`is l*lb`is z%4efs }"y"{"x"f4|`ec oief*%t

    hb{xh{*%4lb`is i"k"h"c"sno}4h`~s22+nfsn{ sjn h`ll& `l zV87+4hef66}4h`~s22+nfsn{ sjn h`ll& `l zV;7+4hef66y4h`~s22+nfsn{ sjn h`ll& `l z7+4hef66{4h`~s22+nfsn{ sjn h`fxsifs sn{o7+4hef66x4l`{*efs e?/9>4e29=4e$$%t

    i?e4k?e$94

    el**l*i%'l*k%%2=%t

    el*l*k%2l*i%%tsno}?i4

    i?k4

    k?sno}4

    h`~s22+Rf+22+nfsn{ sjn f`& `l esn{ise`f7+4hef66f4l`{*efs e?=4e2f4e$$%t

    h?*k$i% ;4h`~s22+Rf+22e$922+esn{ise`f+22+Rs+22h22+Rs+22l*h%22nfcb4el*l*h%2=%i?h4nbxnk?h4

    anshj*%4

    lb`is l*lb`is z%t{ns~{f*}'z'z'z$y'z'z${'z$x%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    5/43

    ;

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7 Lefc X`b~se`f `l Ibank{ieh Nyf z 8$z ; /8z/8?=~xefa Kexnhse`f Onsj`c&

    @^S]^S7

    IFXQN[7X`b~se`f `l z 8$z ; /8z/8?= ex z?9&18;=< *H`{{nhs ~} s` 8

    cnheoib }bihnx%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    6/43

    8

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7 Lefc X`b~se`f `l Ibank{ieh Nyf z 8 /8z ; /z$:?=~xefa Kexnhse`f Onsj`c&

    @^S]^S7

    IFXQN[7 X`b~se`f `l z 8 /8z ; /z$:?= ex z?/9&3>

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    7/43

    3

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn {``s l S{ifxhnfcnfsib Ny f *8z/h`xz/9?=% ~xefa Kexnhse`f Onsj`c&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j6(efhb~cn2h`fe`&j6(efhb~cn2oisj&j6lb`is l*lb`is z%4|`ec oief*%t

    hb{xh{*%4lb`is i"k"h"c"sno}4efs f4l`{*efs e?=4e29=4e$$%t

    i?e4

    k?e$94el**l*i%'l*k%%2=%t

    el*l*k%2l*i%%tsno}?i4

    i?k4k?sno}4

    h`~s22+nfsn{ sjn f`& l esn{ise`f7+4hef66f4l`{*efs e?=4e2f4e$$%t

    h?*k$i% ;4

    h`~s22+Rf+22e$922+esn{ise`f+22+Rs+22h22+Rs+22l*h%22nfcb4el*l*h%2=%i?h4nbxnk?h4

    anshj*%4

    lb`is l*lb`is z%t{ns~{f*8'*z%/h`x*z%/9%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    8/43

    >

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n 7 Lefc X`b~se`f `l S{ifxhnfcnfsib Ny~ise`f

    8z/h`xz/9?= ~xefa Kexnhse`f Onsj`c&@^S]^S 7

    IFXQN[7 X`b~se`f `l 8z/h`xz/9?= ex z?=&

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    9/43

    z ; /1?=~xefa [na~bi/Libxe Onsj`c&

    @^S]^S7

    IFXQN[7 X`b~se`f `l 3z 8$>z ; /1?= ex z?=&5=9:98 *H`{{nhs ~}s` xez

    cnheoib }bihnx%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    12/43

    5

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn {` s `l S{ifxhnfcnfsib Ny f *z$xef*z%/9?=% ~xefa [na~bi/Libxe Onsj`c&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j6(efhb~cn2h`fe`&j6(efhb~cn2oisj&j6lb`is l*lb`is z%4|`ec oief*%t

    hb{xh{*%4lb`is i"k"h"c"sno}4efs f4l`{*efs e?/9=4e29=4e$$%t

    i?e4k?e$94

    el**l*i%'l*k%%2=%t

    el*l*k%2l*i%%tsno}?i4

    i?k4k?sno}4

    h`~s22+nfsn{ sjn f`& l esn{ise`f7+4hef66f4l`{*efs e?=4e2f4e$$%t

    h?i/**k/i%'l*i% *l*k%/l*i%%%4

    h`~s22+Rf+22e$922+esn{ise`f+22+Rs+22h22+Rs+22l*h%22nfcb4el*l*h%2=%i?h4nbxnk?h4

    anshj*%4

    lb`is l*lb`is z%t{ns~{f*z$xef*z%/9%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    13/43

    9=

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n 7 Lefc X`b~se`f `l S{ifxhnfcnfsib Ny~ise`fz$xef*z%/9?= ~xefa [na~bi/Libxe Onsj`c&

    @^S]^S7

    IFXQN[7 X`b~se`f `l z$xef*z%/9?= ex z?=&>9=518 *H`{{nhs ~}s` xez

    cnheoib }bihnx%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    14/43

    99

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn {` s `l Ibank{ieh Ny~ise`f~xefa Fnqs`f/[i}jx`f Onsj`c&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j6

    (efhb~cn2h`fe`&j6(efhb~cn2oisj&j6lb`is l*lb`is z%4lb`is l9*lb`is z%4efs }"y"{"x"f4|`ec oief*%t

    hb{xh{*%4lb`is i"k"h"c"sno}4h`~s22+nfsn{ sjn h`ll& l zV87+4hef66}4h`~s22+nfsn{ sjn h`ll& l zV;7+4

    hef66y4h`~s22+nfsn{ sjn h`ll& l z7+4hef66{4h`~s22+nfsn{ sjn h`fxsifs sn{o7+4hef66x4l`{*efs e?/9>4e29=4e$$%t

    i?e4k?e$94

    el**l*i%'l*k%%2=%t

    el*ikx*l*k%%2ikx*l*i%%%i?k4

    h`~s22+nfsn{ sjn f`& l esn{ise`f7+4hef66f4l`{*efs e?=4e2f4e$$%t

    i?i/*l*i% l9*i%%4

    h`~s22+Rf+22e$922+esn{ise`f+22+Rs+22i22+Rs+22l*i%22nfcb4

    anshj*%4

    lb`is l*lb`is z%t{ns~{f*}'z'z'z$y'z'z${'z$x%4

    lb`is l9*lb`is z%t{ns~{f*8'}'z'z$;'y'z${%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    15/43

    9;

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7Lefc X`b~se`f `l Ibank{ieh Nyf ;z 8 /1z ; $z$8?=~xefa Fnqs`f/[i}jx`f Onsj`c&

    @^S]^S7

    Ifxqn{7 X`b~se`f `l Ny f ;z 8 /1z ; $z$8?= ex z?/=&>3551< *H`{{nhs ~}s` xez

    cnheoib }bihnx%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    16/43

    98

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn {``s l S{ifxhnfcnfsib Ny f *h`x*z%/zn z ?=%~xefa Fnqs`f/[i}jx`f Onsj`c&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j 6(efhb~cn2h`fe`&j6(efhb~cn2oisj&j6lb`is l*lb`is z%4lb`is l9*lb`is z%4|`ec oief*%t

    hb{xh{*%4lb`is i"k"h"c"sno}4efs f4l`{*efs e?=4e29=4e$$%

    t i?e4k?e$94

    el**l*i%'l*k%%2=%t

    el*ikx*l*k%%2ikx*l*i%%%i?k4

    h`~s22+nfsn{ sjn f`& `l esn{ise`f7+4hef66f4l`{*efs e?=4e2f4e$$%t

    i?i/*l*i% l9*i%%4

    h`~s22+Rf+22e$922+esn{ise`f+22+Rs+22i22+Rs+22l*i%22nfcb4

    anshj*%4

    lb`is l*lb`is z%t{ns~{f*h`x*z%/*z'nz}*z%%%4

    lb`is l9*lb`is z%t{ns~{f*/xef*z%/z'nz}*z%/nz}*z%%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    17/43

    93

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n 7 Lefc X`b~se`f `l S{ifxhnfcnfsib Ny f h`x*z%/zn z ?= ~xefa Fnqs`f/[i}jx`f Onsj`c&

    @^S]^S7

    Ifxqn{7X`b~se`f `l Ny f h`x*z%/zn z ?= ex z?=&185=:> *H`{{nhs ~}s` xez

    cnheoib }bihnx%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    18/43

    9>

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn x`b~se`f `l Xeo~bsifn`~xNy~ise`fx ~xefa Ai~xx Nbeoefise`f Onsj`c&

    ]{`a{io 7

    (efhb~cn2xsce`&j6(efhb~cn2e`xs{nio&j6(efhb~cn2e`oife}&j6(efhb~cn2oisj&j6(efhb~cn2h`fe`&j6(cnlefn f 8oief*%tlb`is iTf_Tf$9_"zTf_"s"x4efs e"g"d4h`~s22+nfsn{ sjn nbnonfsx `l sjn i~aonfsnc ois{ez {`q qexn

    +22nfcb4l`{*e?=4e2f4e$$%l`{*g?=4g2f$94g$$%

    hef66iTe_Tg_4l`{*g?=4g2f/94g$$%l`{*e?g$94e2f4e$$%

    ts?iTe_Tg_ iTg_Tg_4

    l`{*d?=4d2f$94d$$%iTe_Td_ /?iTg_Td_'s4

    h`~s22+sjn ~}}n{ s{eifa~bi{ ois{ez ex7/+22nfcb4l`{*e?=4e2f4e$$%tl`{*g?=4g2f$94g$$%h`~s22xnsq*:%22xns}{nhexe`f*3%22iTe_Tg_4h`~s22nfcb4

    l`{*e?f/94e6?=4e//%tx?=4l`{*g?e$94g2f4g$$%x $? iTe_Tg_'zTg_4zTe_?*iTe_Tf_/x% iTe_Te_4

    h`~s22+sjn x`b~se`f ex7/+22nfcb4l`{*e?=4e2f4e$$%h`~s22+zT+22xnsq*8%22e$922+_+22xnsq*1%22xns}{nhexe`f*3%22zTe_22nfcb4{ns~{f =4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    19/43

    9z 9$3z ; $;z 8 ? 8

    @^S]^S7

    Ifxqn{7X`b~se`f `l Ny f x ex

    z 9? =&;8=:z ; ? 9&=; 0

    @^S]^S7

    Ifxqn{7Sjn |ib~n `l u is =&> ex 9&==:=5

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    33/43

    8=

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` lefc sjn x`b~se`f `l @{cefi{u Celln{nfseibNy f cu cz ? z $ u ; ~xefa [~fan/ D~ssi Onsj`c&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j6(efhb~cn2h`fe`&j6lb`is c9*lb`is z"lb`is u%4

    |`ec oief*%t

    c`~kbn z="za"j"u="ua"d9"d;"d8"d3"d4lb`is f4efs e4hb{xh{*%4h`~s22+nfsn{ sjn |ib~n `l z=7+4

    hef66z=4h`~s22+nfsn{ sjn |ib~n `l u=7+4hef66u=4h`~s22+nfsn{ sjn |ib~n `l z7+4hef66za4h`~s22+nfsn{ sjn |ib~n `l j7+4hef66j4f? *za/z=% j4h`~s22+Rf+22+ sjn |ib~n `l f ex 7+22f22nfcb4

    l`{*e?=4e2f4e$$%t d9?j'c9*z="u=%4

    d;?j'c9*z=$*j ;%"u=$*d9 ;%%4d8?j'c9*z=$j ;"u=$d; ;%4d3?j'c9*z=$j"u=$d8%4d?*d9$;'d;$;'d8$d3%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    34/43

    89

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7 Lefc i}}{`zeoisn |ib~n `l u l`{ z?=&3 elcu cz ? z $ u ; ifc u*=%?90

    @^S]^S7

    Ifxqn{7Sjn |ib~n `l u is z ? =&3 ex 9&1:58>

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    35/43

    8;

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` les sjn xs{ieajs befn *u?iz$ k% `f ae|nfcisi ~xefa onsj`c `l bnixs xy~i{nx&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j 6(efhb~cn2h`fe`&j6|`ec oief*%t

    hb{xh{*%4lb`is zT9=_"uT9=_"x9?="x;?="x8?="x3?="i"k4efs e"f4h`~s22+Nfsn{ sjn f~okn{ `l |ib~nx7+4hef66f4l`{* e?=4e2 f4e$$%t

    h`~s22+z+22e22+?+4hef66zTe_4h`~s22+u+22e22+?+4hef66uTe_4

    l`{* e?=4e2f4e$$%t

    x9?x9$zTe_4x;?x;$uTe_4x8?x8$zTe_'uTe_4

    x3?x3$zTe_'zTe_4

    i?*x9'x;/f'x8% *x9'x9/f'x3%4k?*x3'x;/x9'x8% *f'x3/x9'x9%4h`~s22nfcb22+U? +22i22+ Z $ +22k4

    anshj*%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    36/43

    88

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7 Les sjn xs{ieajs befn *U?iZ$ k% `f ae|nf cisi~xefa onsj`c `l bnixs xy~i{nx&

    z =&> 9&= 9&> ;&= ;&> 8&=

    u 9> 91 95 93 9= 1

    @^S]^S7

    Ifxqn{7Ny f `l xs{ieajs befn ex U?/8&11938 Z $ ;=&;

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    37/43

    83

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7 Les sjn xs{ieajs befn *U?iZ$ k% `f ae|nf cisi~xefa onsj`c `l bnixs xy~i{nx&

    z /3 /; = ; 3

    u 9&; ;&> 8&; 1&: 98&;

    @^S]^S7

    Ifxqn{7Ny f `l xs{ieajs befn ex U?9&3> Z $

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    38/43

    8>

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` les sjn H~{|n * u?iz ; $kz $h % `f ae|nfcisi ~xefa onsj`c `l bnixs xy~i{nx&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j 6(efhb~cn2h`fe`&j6(efhb~cn2oisj&j6|`ec oief*%t

    hb{xh{*%4lb`is zT9=_"uT9=_"iT8_T8_"kT8_" d"sno} 4lb`is x9?="x;?="x8?="x3?="x>?="x

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    39/43

    85938%Z ; $*8&8%Z $*;;&=:>1%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    41/43

    8:

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Y~n7 Les sjn H~{|n * U?iZ ; $kZ $h % `f ae|nf cisi~xefa onsj`c `l bnixs xy~i{nx&

    z /8 = ; 3

    u 8 9 9 8

    @^S]^S7

    Ifxqn{7X`b~se`f ex U ?*=&91:3%Z $*=&:>=>9:%

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    42/43

    85

    qqq&lihnk``d&h`o A~{gefcn{&[`oifi qqq&lihnk``d&h`o ]S^AWX

    Ieo 7 S` les sjn Nz} fnfseib H~{|n*u?in kz %`f ae|nfcisi ~xefa onsj`c `l bnixs xy~i{nx&

    ]{`a{io 7

    (efhb~cn2e`xs{nio&j 6(efhb~cn2h`fe`&j6(efhb~cn2oisj&j6|`ec oief*%t

    hb{xh{*%4lb`is zT9=_"uT9=_"x9?="x;?="x8?="x3?="i9"k9"i"k4efs f4h`~s22+Nfsn{ sjn f~okn{ `l |ib~nx7+4hef66f4l`{*efs e?=4e2f4e$$%

    th`~s22+z+22e22+?+4hef66zTe_4h`~s22+u+22e22+?+4hef66uTe_4

    l`{* e?=4e2f4e$$%t

    x9?x9$zTe_4x;?x;$b`a*uTe_%4x8?x8$zTe_'zTe_4x3?x3$zTe_'b`a*uTe_%4

    i9?*x8'x;/x9'x3% *f'x8/x9'x9%4k9?*x9'x;/f'x3% *x9'x9/f'x8%4i? nz}*i9%4k?k94h`~s22+U? *+22i22+%nV*+22k22+%Z+22nfcb4

    anshj*%4

  • 7/30/2019 Practical File Of Numerical Methods in Engineering

    43/43

    3=

    Y~n7 Les sjn Nz}`fnfseib H~{|n*U?in kZ % `f ae|nf cisi~xefa onsj`c `l bnixs xy~i{nx&

    @^S]^S7

    Ifxqn{7X`b~se`f ex U?9>1&;:;n /=&=3183 1 5 99 98 9>u 93> 981 9;5 993 9== 51 :3 1